Looks like spider mite webbing to me, though I could be wrong. Did you notice it after it had been indoors for a little while? Sometimes, they seem to pop out of nowhere on houseplants, and favor very dry conditions (ie, indoors). They can damage plants. I'd recommend using a cotton tip applicator to remove all webbing you see, misting it with very diluted soapy water (like a dime-sized drop of gain dish soap in a small spray bottle), increasing humidity for your orchid (ie, misting it), and inspecting nearby plants for similar webbing with the abovementioned treatment. Be sure to inspect your houseplants again a week afterward to check for any new webbing, as they sometimes come back. Here's more information:
I've dealt with spider mites on a number of my houseplants during the winter, and I've been able to treat them pretty successfully.